A hyper-Kähler metric on the moduli spaces of monopoles with arbitrary symmetry breaking
arXiv:2306.03069 · doi:10.1007/s10455-024-09954-z
Abstract
We construct the hyper-Kähler moduli space of framed monopoles over for any connected, simply connected, compact, semisimple Lie group and arbitrary mass and charge, and hence symmetry breaking. In order to do so, we define a configuration space of pairs with appropriate asymptotic conditions and perform an infinite-dimensional quotient construction. We make use of the b and scattering calculuses to study the relevant differential operators.
43 pages, 2 figures. Updated with minor changes and corrections to match the version published in Annals of Global Analysis and Geometry